Exercise 3 solution

    from datetime import datetime, timezone, timedelta

    EPOCH = datetime(1970, 1, 1, tzinfo=timezone.utc)

    def to_us(dt):
        d = dt - EPOCH
        return (d.days * 86400 + d.seconds) * 1_000_000 + d.microseconds

    def from_us(us):
        return EPOCH + timedelta(microseconds=us)

    moments = [
        datetime(2026, 11, 2, 12, 0, 0, 123456, tzinfo=timezone.utc),
        datetime(1969, 7, 20, 20, 17, 40, tzinfo=timezone.utc),
        datetime(2000, 1, 1, tzinfo=timezone.utc),
        datetime(1970, 1, 1, tzinfo=timezone.utc),
    ]
    for m in sorted(moments):
        us = to_us(m)
        print(us, from_us(us) == m)
    m = moments[0]
    secs, us = divmod(to_us(m), 1_000_000)
    days, rem = divmod(secs, 86400)
    print("Days since epoch:", days, "seconds into day:", rem, "microseconds:", us)
    a = datetime(2016, 12, 31, tzinfo=timezone.utc)
    b = datetime(2017, 1, 1, tzinfo=timezone.utc)
    print("Days between:", (to_us(b) - to_us(a)) // 1_000_000 // 86400)
    print("Seconds between:", (b - a).total_seconds())
    try:
        datetime(2016, 12, 31, 23, 59, 60, tzinfo=timezone.utc)
    except ValueError as e:
        print("ValueError:", e)

Output (run, and exactly as shown):

    -14182940000000 True
    0 True
    946684800000000 True
    1793620800123456 True
    Days since epoch: 20759 seconds into day: 43200 microseconds: 123456
    Days between: 1
    Seconds between: 86400.0
    ValueError: second must be in 0..59, not 60

Explanation: integer microseconds round-trip exactly, which a float of
seconds cannot promise at nanosecond scale. Dates before 1970 give negative
values and still sort correctly. divmod splits a count into whole days, seconds
into the day and microseconds. Unix time pretends every day has exactly 86400
seconds: the day containing the 2016 leap second is still 86400 seconds long
by the timestamps, and Python's datetime refuses a second value of 60, so a
leap second can never appear as its own moment.